The term Old Catholic was used first in 1853 to describe members of the See of Utrecht who did not recognize infallible papal authority. The 1st Vatican Council officially approved this doctrine in 1870. The Catholics who refused this new doctrine joined together and formed the Union of Utrecht. The Old Catholic Church believes in unity through diversity. In 1908 Fr. Arnold Mathew was ordained as a Regionary Bishop of England. He was sent to serve under Bishop Rudolph de Landas Berghes as a missionary in the U.S. Berghes was placed under the jurisdiction of Episcopal Bishop Fond du Lac, who the Old Catholic Church, was and is is, in full communion with. There were many historical rabbit holes to crawl in and out of but the core member communities moved steadily toward ecumenism. They slowly moved to the ordination of women and open attitudes toward the LGBT community. Some hard core factions separated and remain independent today such as the Polish National Catholic Church.
Old Catholicism maintains apostolic succession by its original ties to Rome. The liturgy is almost identical to Rome. The first women were ordained by German Bishops on May 27, 1996. Except for rare teachings from the likes of Bishop Urs Kury transubstantiation (Rome) and consubstantiation (Luther ) are accepted. Clergy can be married and divorced persons can have a new religious marriage. There is no teaching on abortion or birth control, leaving these types of decisions to the married couple.
In the U.S. there are many churches whose ties are to the Old Catholic Church and remain in communion with them. You can fine these by goggling names such as:
Primitive Catholic Church
Reformed Catholic Church
North American Old Catholic Church
Independent Catholic Church
Ecumenical Catholic Church
For myself, I completed 5 years of roman seminary and was ordained a Deacon in 2000. Two years ago in New Orleans I was ordained a priest by the current Vicar General of the reformed Catholic Church.
There are many progressive options in the modern Catholic tradition. Happy hunting all who are so inclined.